Apply gypsum if you have determined a need for it via a soil test. Also it doesn't break down clay, it helps to flocculate it in some cases.

Yes, very true about a soil test. It does, however, over time, trend toward easing compacted clay soils combined with aeration. Some of our clay soils are very acidic so the gypsum helps with the ph.
When I working down south(Bama, Florida) we would bring in sandy loam to top dress about the time the warm season grasses were waking up from winter. A thin layer, less than 1/4 inch in any areas that were tracked or just low. After a few cuts, the yard was mostly level and no eveidence that was done.
Here, spring growth is crazy and just dont see much of that happening here. Golf Courses, yes, but residental and commercial, no. Complete yard renovations I see from time to time.